# Help finding eigenvectors to simple 2x2 matrix

#### NCyellow

1. Homework Statement
Find a fundamental set of real solutions of the system.
x'=[-0.5 1 ]x
[-1 -0.5]

3. The Attempt at a Solution
I calculated the eigenvalues to be r1 = -0.5+i and r2 = -0.5-i
Then, attempting to calculate the eigenvectors,
I plugged the numbers into the system
[-0.5+0.5-i 1][v1] = [0]
[-1 -0.5+0.5-i ][v2] [0]
which simplifies to be
[-i 1] [v1] = [0]
[-1 -i ][v2] [0]
afer matrix multiplication, I get two formulas
-1(v1)i+(v2)=0
-1(v1)-(v2)i=0
However, I am at a loss for the next step. Usually when I am finding the eigenvector those two equations will have the same ratio. Please advise.

Related Calculus and Beyond Homework Help News on Phys.org

#### gabbagabbahey

Homework Helper
Gold Member
Your two formulas do have the same ratio...Just multiply the second equation by $i$.

#### NCyellow

thanks guy! I can't believe i didn't see that!

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving